Question

It has been reported that the percentage of American households with children under 18 living at home has hit its lowest point at 46% in half a century.

1. How many households do you expect will have children under 18 living at home in a sample mean of 1000?
2. Calculate the standard deviation of the same proportions
3. What is the probability that in a sample of 1000 households there are between 450 and 470 observations that have children under 18 living at home?

MUST SHOW ALLLL WORK!!!!!!!!!!!!!!

Answer 1

Solution

Given that,

p = 0.46

1 - p = 1 - 0.46 = 0.54

n = 1000

a) x = n * p = 1000 * 0.46 = 460 households

b)   = p = 0.46

  [p ( 1 - p ) / n] = [(0.46 * 0.54) / 1000 ] = 0.0158

c) P( 0.45 < < 0.47)

= P[(0.45 - 0.46) /0.0158 < ( - ) / < (0.47 - 0.46) / 0.0158 ]

= P(-0.63 < z < 0.63)

= P(z < 0.63) - P(z < -0.63)

Using z table,   

= 0.7357 - 0.2643

= 0.4714